BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Stephen Muirhead (Univ. Melbourne\, Australia) DTSTART:20200916T100000Z DTEND:20200916T104500Z DTSTAMP:20260421T174209Z UID:BPS/12 DESCRIPTION:Title: On the number of level sets of smooth Gaussian fields - II\nby Stephen Mu irhead (Univ. Melbourne\, Australia) as part of Bangalore Probability Semi nar\n\n\nAbstract\nLevel sets of smooth Gaussian fields appear in many are as of mathematics. They have numerous applications outside of mathematics from astrophysics to oceanology to biology. Probably the first significant progress in the study of level lines came in 1940s when Kac and Rice deve loped formulas that allow to compute the expected number of roots of a ran dom function in 1d. These formulas can be generalised to higher dimension where they allow to compute the expected volume of level sets. Unfortunate ly\, these formulas do not allow to study the number of level lines since it is a non-local quantity which can not be written as a Kac-Rice-type int egral formula. In this talk we will discuss recent progress in the study o f the number of level lines for smooth Gaussian fields. \n\nIn the first p art of the talk D. Belyaev will give a gentle introduction to the area and give a broad overview of recent results. In particular\, he will describe how the number of level lines depends on the level. This allows to show t hat the expected number of lines depends (almost) smoothly on the level an d allows to give a low bound on the fluctuation of the number of level lin es. In the second part S. Muirhead will explain in more details the ideas behind these results and will sketch the proof of the variance bound.The t alk is based on a series of papers by D. Belyaev\, M. McAuley and S. Muirh ead.\n LOCATION:https://researchseminars.org/talk/BPS/12/ END:VEVENT END:VCALENDAR